Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes

Charles F. Laywine; Gary L. Mullen

doi:10.1016/0097-3165(92)90050-5

Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes

Charles F. Laywine, Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Using affine resolvable designs and complete sets of mutually orthogonal frequency squares and hypercubes, we provide several generalizations of Bose's equivalence between affine planes of order n and complete sets of mutually orthogonal latin squares of order n. We also characterize those complete sets of orthogonal frequency squares and hypercubes which are equivalent to affine geometries.

Original language	English (US)
Pages (from-to)	13-35
Number of pages	23
Journal	Journal of Combinatorial Theory, Series A
Volume	61
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(92)90050-5
State	Published - Sep 1992

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0097-3165(92)90050-5

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title = "Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes",

abstract = "Using affine resolvable designs and complete sets of mutually orthogonal frequency squares and hypercubes, we provide several generalizations of Bose's equivalence between affine planes of order n and complete sets of mutually orthogonal latin squares of order n. We also characterize those complete sets of orthogonal frequency squares and hypercubes which are equivalent to affine geometries.",

author = "Laywine, {Charles F.} and Mullen, {Gary L.}",

note = "Funding Information: In this paper we prove several generalizations of this result. In attempting to generalize Bose{\textquoteright}s result, one might proceed in several * This author would like to thank the Natural Sciences and Engineering Research Council of Canada for partial support under Grant No. OGPOO14645. + This author would like to thank the National Security Agency for partial support under Grant Agreement MDA904-87-H-2023.",

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T1 - Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes

AU - Laywine, Charles F.

AU - Mullen, Gary L.

N1 - Funding Information: In this paper we prove several generalizations of this result. In attempting to generalize Bose’s result, one might proceed in several * This author would like to thank the Natural Sciences and Engineering Research Council of Canada for partial support under Grant No. OGPOO14645. + This author would like to thank the National Security Agency for partial support under Grant Agreement MDA904-87-H-2023.

PY - 1992/9

Y1 - 1992/9

N2 - Using affine resolvable designs and complete sets of mutually orthogonal frequency squares and hypercubes, we provide several generalizations of Bose's equivalence between affine planes of order n and complete sets of mutually orthogonal latin squares of order n. We also characterize those complete sets of orthogonal frequency squares and hypercubes which are equivalent to affine geometries.

AB - Using affine resolvable designs and complete sets of mutually orthogonal frequency squares and hypercubes, we provide several generalizations of Bose's equivalence between affine planes of order n and complete sets of mutually orthogonal latin squares of order n. We also characterize those complete sets of orthogonal frequency squares and hypercubes which are equivalent to affine geometries.

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Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes

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